1. Field of the Invention
The present invention relates to transfer functions across an electrical system. More specifically, the present invention relates to digital synthesis of transfer function impedance.
2. Present State of the Art
A transfer function operates on a given input to produce a certain output and is often represented as the ratio of the output to the input. Frequently, differential equations are used to represent or describe not only the input and the output, but also the relationship between them. Solving and representing systems and transfer functions with differential equations involves a complicated mathematical analysis and is, in general, not very satisfactory. For that reason, transfer functions are often designed and analyzed using Laplace transforms of the input, the output and the transfer function.
The Laplace transform significantly simplifies the analysis of a transfer function because the system input and output can be algebraicly manipulated. Similarly, the ratio of the output to the input, or the transform function, can also be altered using algebraic principles. After the transform function has been analyzed in the Laplace domain, it is converted to the time domain in many instances. In many systems, including electrical, mechanical, and electro mechanical systems, the transfer function is found by providing an input, measuring the output, and calculating the ratio of the output to the input. In other circumstances, the transfer function is known, and only the physical implementation of the transfer function needs to be designed. In either case, this analysis is typically performed in the Laplace domain using Laplace transforms.
While a transfer function may be found mathematically, the actual or physical implementation of the transfer function is quite different. With regard to electrical systems, a transfer function represents the effect that a combination of electrical circuit elements such as capacitors, inductors and resistors has on an input signal. When these elements are inserted into a circuit, their effect is to create an impedance which acts upon the input signal to produce the output signal.
Once a transfer function has been physically implemented with the circuit elements, however, there are several limitations. For instance, if a different output is desired or it is discovered that the current implementation of the transfer function is incorrect or inadequate, then a new circuit which does implement the desired transfer function has to be designed. This entails additional cost and time. Also, the resistors, capacitors and inductors used to construct the circuit require physical space, which can be crucial in some electrical applications such as PCMCIA compliant network and modem cards. Further, many circuit elements are manufactured such that resistance, capacitance or inductance is within specified tolerances. As a result, the transfer function implemented with passive circuit elements may not be sufficiently accurate due to the tolerances of the circuit elements. Accuracy can, of course, be improved with items such as precision resistors, but extra precision increases the cost of the circuit substantially in some instances.
It is therefore desirable to have as circuit which not only increases the accuracy of the transform function, but also is able to implement additional transform functions or alter the current transform function without additional circuitry and without additional design.
It is therefore an object of one embodiment of the present invention to digitally synthesize an impedance.
It is yet another object of one embodiment of the present invention to digitally convert an input signal to an output signal.
It is a further object of one embodiment of the present invention to synthesize an impedance representative of a transfer function.
It is another object of one embodiment of the present invention to be able to synthesize an impedance of more than one transfer function.
It is a further object of one embodiment of the present invention to generate a current having a value related to the impedance of the transfer function.
In summary, a transfer function is described as the ratio of an output to an input. In electrical circuitry, the transfer function is frequently defined in terms of an output voltage related to an input voltage. Often the transfer function is known and only the circuitry representing the transfer function needs to be designed. This circuitry is subject to component tolerances, and must be redesigned for each separate transfer function.
A transfer function has an impedance which can be represented as a shunt impedance across the output. In one embodiment of the present invention, an input voltage is sensed and a current is generated which is related to the sensed voltage such that the impedance of the transfer function is present as defined by the sensed voltage divided by the generated current. The impedance of the transfer function is created by converting the sensed voltage to a digital value and then processing it with a generator that produces a voltage that is related to the desired impedance. The generator is implemented in software and uses the impedance of the transform function to alter the sensed voltage. This voltage produced by the generator is converted to an analog voltage and connected to a voltage controlled current source. The generator causes the voltage controlled current source to produce a current having the inverse value of the transform function impedance. In this manner, a shunt current is generated. The shunt current has a value equal to the inverse of the impedance of the transfer function and by Ohm""s law, the impedance created by the circuitry of this embodiment has a value equivalent to the impedance of the transfer function. In this manner, the impedance of a transfer function is digitally synthesized.
The advantages of this design are several. The circuitry has no circuit elements in series between the input and the output and direct current voltage drops are therefore not present. Additionally, many different transfer functions can be digitally synthesized by using a different generator. Also, many systems already have many of the circuit components necessary to perform the impedance synthesis, including processors, ADCs and DACs. In this manner, cost is minimized and circuit board space is preserved.
Additional objects and advantages of the present invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the instruments and combinations particularly pointed out in the appended claims. These and other objects and features of the present invention will become more fully apparent from the following description and appended claims, or may be learned by the practice of the invention as set forth hereinafter.